Hi ROU,
As far as I've been able to make out, based on various sources but probably a bit unreliable…
Royalists-
-Approximately 3000 foot and 1000 horse
-Supposedly had 5 regiments of trained bands, with only 800 muskets between them
-Strickland's Gower's and Metham's Yorkshire Trained Bands
-Possibly Pennyman's YTB that might have been in the process of converting into the volunteer regiment.
-Possibly the Lord General's foot being raised (Lindsey's at this time)
- various horse, including the King's Lifeguard, Prince of Wales, Gower, Wortley, and Newcastle's troops and Duncombe's dragoons
-Possibly Legge, Wilmot, Glemham, and Willoughby's troops
-14 guns
Parliamentarians
About 3000 foot by the end comprised of-
1000 of the garrison under Hotham, being the East Riding of Yorkshire Trained band, see here link with over 1000 men according to their musters:
11.07.42 10 Companies 102 Officers 1292 men
18.07.42 11 Companies 113 Officers 1530 men
25.07.42 14 Companies 142 Officers 2031 men
500 brought by Meldrum
1500 landed later by ships of Trenchfield, who bombarded the Royalists for good measure, his ships were the Hercules, Rainbow and Unicorn,
Not sure of regiments for these
Possibly some foot belonging to Ayscough and Boynton though I'm not sure they were raised by this stage.
-Lots of canon
As ever would be really interested to hear if anyone has found more on this, and always welcome input at the BCW Regimental Wiki here wiki.bcw-project.org/start
